Great Amusements Park has been raising its ticket prices every year, as shown in the table below

Year. Price

0. 50

1. 55

2. 60.50

3. 66.55

1. Describe how the ticket prices are growing.

2. What will the price of admission be in year 6?

1.)

Between year 0 and year 1, we went from $50 to $55.

$55/$50 = 1.1

The price increased by 10% from year 0 to year 1.

Between year 2 and year 1, we went from $55 to $60.50.

$60.50/$55 = 1.1

The price also increased by 10% from year 1 to year 2. If we investigate this for each year, we will see that the price increases consistently by 10% every year.

The sequence can be written as an = 50· (1.1) ⁿ

2.) To determine the price in year 6, we can use the sequence formula we established already.

a6 = 50· (1.1) ⁶ = $88.58

The price of the tickets in year 6 will be $88.58.